{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial 2: Fields and Operators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This tutorials covers the basics of setting up and interacting with field and operator objects in Dedalus."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we'll import the public interface and suppress some of the logging messages:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from dedalus import public as de\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "de.logging_setup.rootlogger.setLevel('ERROR')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.1: Fields"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating a field"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Field objects represent scalar fields defined over a domain.  A field can be directly instantiated from the `Field` class by passing a domain object, or using the `domain.new_field` method.  Let's set up a 2D domain and build a field:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "xbasis = de.Fourier('x', 64, interval=(0,2*np.pi), dealias=3/2)\n",
    "ybasis = de.Chebyshev('y', 64, interval=(-1,1), dealias=3/2)\n",
    "domain = de.Domain([xbasis, ybasis], grid_dtype=np.float64, mesh=[1])\n",
    "f = domain.new_field(name='f')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also gave the field a name -- something which is automatically done for the state fields when solving a problem in Dedalus (we'll see more about this in the next notebook), but we've just done it manually, for now."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Manipulating field data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `layout` attribute of each field is a reference to the layout object (discussed in tutorial 1) describing the current transform/distribution state of that field's data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.layout.grid_space"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Field data can be written and retrieved in any layout by indexing a field a layout object.  In most cases it's just the full grid and full coefficient data that's most useful to interact with, and these layouts can be easily accessed using `'g'` and `'c'` keys as shortcuts.  Field objects also have several methods that can be used to convert the data between layouts.\n",
    "\n",
    "Remember that when accessing field data, you're manipulating just the local data of the globally distributed dataset.  Details about the data distribution are available through methods on the layout objects.\n",
    "\n",
    "Let's assign our field some data using the local domain grids."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x, y = domain.grids(scales=1)\n",
    "# Set data in grid space using 'g' key\n",
    "f['g'] = np.cos(4*x) / np.cosh(3*y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And let's take a look at this data using some helper functions from the `plot_tools` module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from dedalus.extras.plot_tools import plot_bot_2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kburns/Dropbox/Git/dedalus/dedalus/extras/plot_tools.py:116: MatplotlibDeprecationWarning: You are modifying the state of a globally registered colormap. In future versions, you will not be able to modify a registered colormap in-place. To remove this warning, you can make a copy of the colormap first. cmap = copy.copy(mpl.cm.get_cmap(\"RdBu_r\"))\n",
      "  cmap.set_bad('0.7')\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_bot_2d(f);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's take a look at the magnitude of the coefficients:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convert data to coefficient space by indexing with 'c' key\n",
    "f['c']\n",
    "# Plot log of magnitude of data\n",
    "def log_magnitude(xmesh, ymesh, data):\n",
    "    return xmesh, ymesh, np.log10(np.abs(data))\n",
    "plot_bot_2d(f, func=log_magnitude);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the specified function is pretty well-resolved.\n",
    "\n",
    "In addition to the key interface, we can change the layout of a field using the `require_coeff_space`, `require_grid_space`, `require_layout`, and `require_local` methods."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Field scale factors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `set_scales` method is used to change the scaling factors used when transforming field data into grid space.  When setting a field's data using grid arrays, shape errors will result if there is a mismatch between the field and grid's scale factors.\n",
    "\n",
    "Large scale factors can be used to interpolate the field data onto a high-resolution grid, while small scale factors can be used to view a lower-resolution grid representation of a field.  *Beware: using scale factors less than 1 will result in a loss of data when transforming to grid space.*\n",
    "\n",
    "Let's take a look at a high-resolution sampling of our field, by increasing the scales."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f.set_scales(2)\n",
    "f['g']\n",
    "plot_bot_2d(f);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2: Operators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Arithmetic with fields"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mathematical operations on fields, such as arithmetic, differentiation, integration, and interpolation, are represented by `operator` classes.  An instance of an operator class represents a specific mathematical operation, and provides an interface for the deferred evaluation of that operation with respect to it's potentially evolving arguments.\n",
    "\n",
    "Arithmetic operations between fields, or fields and scalars, are produced simply using Python's infix operators for arithmetic.  Let's start with a very simple example of adding a scalar to the field we previously defined."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Add(<Scalar 140538584019912>, <Field 140538577469848>)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "add_op = 10 + f\n",
    "add_op"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The object we get is not another field, but an operator object representing the addition of 10 and our field.  To actually compute this operation, we use the `evaluate` method, which returns a new field with the result.  The dealias scale factors set during basis instantiation are used for the evaluation of all operators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "add_result = add_op.evaluate()\n",
    "add_result.require_grid_space()\n",
    "plot_bot_2d(add_result);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Building expressions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Operator instances can be passed as arguments to other operators, building trees that represent more complicated expressions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Add(Mul(<Scalar 140538583971544>, Add(<Scalar 140538584019912>, <Field 140538577469848>)), Mul(<Field 140538577469848>, <Field 140538577469848>))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree_op = 2*add_op + f*f\n",
    "tree_op"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reading these signatures can be a little cumbersome, but we can plot the operator's structure using a helper from dedalus.tools:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from dedalus.tools.plot_op import plot_operator\n",
    "plot_operator(tree_op, figsize=8, fontsize=12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And evaluating it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Z/FEwnrdaPC3dNd3RVpwmtzNdumuaC8Zz1zQKJueaS9OQS+4dreeurTfIc5deZ567KK9ry5PtTeW1C/psGRwAzjLrZwIHnWMvIukiUtWD5e+7gCspup2CIAiCGeizZXAtcI6InA3cQfEP/8fTg0TkROAHgFeYbbuBgareXy6/EPj1WlhgcTB9NNGKqXEXKncneXcXq5lzwVTuNFb9yU7scTYN9nzp3clq5l2IPZ/Na+WuI3M0kectDdNEjrvanZjjLj0ux11bb+C7axpN1OU1B3nu2l5z6XFdXnPQ9Mwgyivkl9cu6K0yUNVVEbkE+DjF0NIrVPUGEXl9uf+y8tCXAp9Q1QdN8NOBK8uXPRaA96rqxzYv9UEQBPNFr+8ZqOpVwFXJtsuS9XcB70q23Qo86WjnFxF2LhQ168q4Wsvv0EmNe9jcAcwy70llPpJRNR673jTviX2L0YYZOOGbaPpEo72j2LFg+yDTUR6Tfdad5y2Np6271KPnTpI7wy7dNd2Jee6sN8hzN+scTznumuZ4yrnmpp3DI8ed9Qa+uyivBbnltQviDeQgCIIgKoMgCIJgzieqG8ikaTUYJd0JpnVYGd6WOfHVyGlCNn0sY2zGx9W+qTqwy87DrqSp6r3UUptawr6sYoenmUh3DIeVMLYZat153tJ42rqrPUB23CW9Mlnuml4G8iYJqw2JdNylzfccd00T/lnSdOe4s97Ad+d5S+Np6y7tRvPcRXktyC2vXRAtgyAIgmC+WwYCLJS1bDoCbWweSD1kxq2ldy45NN3RVh7sNQxVs3cNYpKw0HDuXGye7AOpneaB1NKC/+KLded5S+PJxXNXe7DnuEvvtrp053kD3136AlmOu1m8QZ67ttdceu5ccq458N1FeV1bziuvXRAtgyAIgiAqgyAIgmDeu4lkMmtpOuW4OmN2c8cte99RrXdv5M0ZY986tGGaxoznPpCqzm/ijFtumB/FuvO8pfG0dWcdQP6spTnuch+Cet7Ad1f77kGGu9z3DNJ057jLnbXU81aLp6W72nsGjrsorwW55bULomUQBEEQzHnLAFgqa9ZkhF1lvnT7wKYyF0junYY5efrQyXuwVxvSZuKSgb3rMHcao9nuNBac4WkL5ril2l2+SYOJxvOWxtPWXdODvcoDwCSeHHe5d7eeN/DdpS2DHHe1eY9yWwYZ7tI7X8+d560WT0t3C0nePHdRXgtyy2sXRMsgCIIgiMogCIIgmPduIjHdRMmQ4ZGpBnd6DwNneCBVe+vQRLy6MvkoR9rsFKfZuWDGV8/6QMobq2y3LzW8BWvded7S87V1l3ZveO6koZvIc5fb1dE0Pt5zl+Y7x13t4f0MD5A9d9Yb+O48b2k8bd2lefXcRXktyC2vXRAtgyAIgiAqgyAIgmAbdBPtWOsmSppVYybNwZ2L078tmjs/emUEQjI+fnV5ZPbZ0QnV5rsMJhNPifnG68Li0ITJe7291uw0ebJ53WFeaU/Hf9vBCtad5y2Np607663YN92d9QbduvO8ge8uHeSR4y6dBK9Ld/XRMtPded7SeJrIcbcjmUbBcxfltSC3vHZBry0DETlfRL4kIreIyKVT9j9HRO4Vkc+VP2/JDRsEQRDk01vLQESGwNuB84ADwLUisl9Vb0wO/RtVffGMYYMgCIIM+uwmOhe4pfyEJSLyfuBCIOcfelbYgQi7ymZW+jHqkU4f+dA0tUAlvPNySvoR7XFl3/L6clOzczzYMfV8tVfnvdEJ4o9OqIxIGNpRC8mLL+Y4687zlq63dTdOp0Rw3KXdRDnuGkfEyNGvC/DdpS9V5bhrmgrEkqY7x531Br47z1saT1t36ctSnrsor/XlpvLaBX12E+0DbjfrB8ptKc8Qkc+LyF+KyHcfY9ggCIIggz5bBtOqtrTq/CzwWFV9QEQuAP4COCczbBAEQZBJn5XBAeAss34mcNAeoKr3meWrROSPRORROWEBZDxisPwQAEvDxcq+kflsXLX5ZT6p19DsrMxo2NQ0XF2dHLeybMJUm++DhaVJGNMEHY0WTBh/HpXKuSRtipuPYti8muUlXa2EYXnFhJm487yl8bR1Z72B7856gzx3TaM8bLo9b9Dgzngrwh3dXfpCm+euNgNphjvrrQgz3Z3nLY2nrbudiUfPXZTXguzy2gF9dhNdC5wjImeLyBJwEbDfHiAiZ4gUpkTkXIr03pMTNgiCIMint5aBqq6KyCXAx4EhcIWq3iAiry/3Xwb8GPDTIrIKPAxcpMX741PD1iMZMzjyQLGY3EHu2HXS+vLSYFKDN40Zt9hXzSuv66cPpMwdxWj5YZO0dJoA82DP3AWNVifpTl9vT9e9dNs82dfY7XZ5+L5KGLEPz4w7z1t6vrbu0jsxz13twV6GO89bmm7PW7rPupP0gW2Gu6Z3PCxNf3/PnfUGvjvPWxpPW3dpXj13UV4LcstrF/T60pmqXgVclWy7zCz/IfCHuWGDIAiC2YjpKIIgCII5n45iPGJw+F4AdGFnZZ8OTfPd7KvMEjj060o726H9iEU6S+ToyKSpaZug46TZObAPoUyY1aVdU+NJ02BJ023zZJuaaw/XAQaH76+EkdXDk3iMH89bGk9bd9YB+O4GyXsGOe48b2m6PW/gu7PeIM9dbUZUx12a7hx3aXeb587zlsbT1p31Br67KK8FueW1C6JlEARBEERlEARBEMx5NxHjETz4bQAGSdNXzTjmnXsm++w3R5vGLdtRCE2jYOz6qh2dMKo2O8dmRELlVXc7umG12nROR0J46bZ5sq+xDx6YjEgYPHxvJYyatFp3nrc0nrbuUo+eO+sN8tx53tJ0e97Ad6fJ6J0cd+n3lT13abpz3K2mo4kcd563Ip7u3Flv4LuL8lqQW167IFoGQRAEQVQGQRAEQVQGQRAEAXP+zEBHK4y+dRcAg527K/sGi5NpZxf3PHp92c4FstjwSqPaD53baW9X/L5uu6/25ux40u+4OpiEWTBh0nlU1Om+TdNdyZP5YtTgyGR42vjeuythxocfnBxn3HneavG0dJf2dXvurDfIc+d5S9PteQPfnfUGee7SeY88d2m6c9yl16PnzvOWxtPWnfUGvrsor+W+zPLaBdEyCIIgCKIyCIIgCOa9m2h1hdE9Xy+Wdx5X2bewyzTfj580TxcGdthaQ7PTvtHYNFTNmQZXx9U2owycL1BVhgwmzU7vjcYk3fYF18Gy6cYoh90CjO45VE334cnbjtad562Ipzt3TVMvW3fWW7F+dHeNb9GadLvewHVnvUGeO+stTUPlXOkbyBnu6l86m+6uaWhpp+6MN/DdRXktyC2vXRAtgyAIgiAqgyAIgmDeu4lWVli+s2hOLe6pjk6Q3SdMlk8+c315ack0RxveaBw7H9hO54+vNhsnX3Jq+sC2XbbnS0cnePOjp+leMhNhyZFJs3NtpBWw3p22xsoDk+OsO88bdOuu3lUx3Z0M/DeQPXdNc/LbdHvewHdnvUGeO+stTYMlTXeOO+sNfHeetzSetu6sN/DdRXktz51ZXrsgWgZBEARBVAZBEARBz91EInI+8PsUn668XFXfmuz/CeBN5eoDwE+r6ufLfbcB9wMjYFVVn5aef7S8yv1fuxOAHSftqew7/viT1pcXD08mgFradfpke8P86GNn4qtRQ/eG3ZdOfCXOxFejysRX6Sf6pr/FkqbbvsQyMHldMc3OBw9Wm+9Hvv3A+rJ153mDbt2l3RueO2mYqM5z53lL0+15A9+d9QZ57qy3NA2WNN057tLr0XPneUvjaetuJekm8txFeS3ILa9d0FtlICJD4O3AecAB4FoR2a+qN5rD/gX4AVX9loi8CPhj4Olm/3NVtftX8YIgCLYZfXYTnQvcoqq3quoy8H7gQnuAqv69qn6rXP0McCZBEARB5/TZTbQPuN2sH6B615/yGuAvzboCnxARBf6Hqv5xGmC8ssIDd3wDgJUHq58j3HnqievLS0cmzVM7f3jTSyzjyksseS9LpfssdrTC2L7E0vAC0TjzJRabJzF5Xbn7zvXlB+6oNrCOfHsyD4p153lL42nrrullIEs6yiPHnecNqun2vIHvznqDPHfptxI8d2m6c9y1veZq52vpznoD312U14Lc8toFfVYG0/5yU22JyHMpKoPvN5ufpaoHReQ04GoRuVlVr9mAdAZBEMw9fXYTHQDOMutnAgfTg0Tke4DLgQtV9Z617ap6sPx9F3AlRbdTEARBMAN9tgyuBc4RkbOBO4CLgB+3B4jIdwAfBl6pql8223cDA1W9v1x+IfDraQSjIyPu/WrxebjjHqw22Xafccr68s571+sYFk311Dwlrml2Nkx1Ozbr6ixDMr+Jc1x9OmKn2ZlOiWxWRyavD9/1rfXlB+64xwbhobsnL89Yd5436NbdOPHjuUtfOstx53lL0+15A9+d9QZ57qy3NA2WNN057tLrzHPXFKZLd9Yb+O6ivBbkltcu6K0yUNVVEbkE+DjF0NIrVPUGEXl9uf8y4C3AqcAfSfGW3toQ0tOBK8ttC8B7VfVjPWQjCIJgLuj1PQNVvQq4Ktl2mVl+LfDaKeFuBZ604QkMgiDYJsQbyEEQBMF8T1Q3Whlz34HiDb7Vh1cr+/bs++b68on3f3t9WVaPrC8vDvy60vb/VfoJG4ZEpv2O1fNN72uszqme9v96Q9Wq6bZ5Gpu8Pvj1iYP7bq8OiXzonsnc8tad5y2Np627ps81Nm3PcdfY723S7XkD3531BnnubDxpGixpunPctb3m0uPaurPewHcX5bU8X2Z57YJoGQRBEARRGQRBEATz3k20Ouab9xTD1UbL1UmiDt9z7/ry+IFvry8PR5Nm3jAZtmgZO83O9PN4TcPTPLzz1YfBTW92pvN1icnTyOTVOrj/UPUN23vvnzRVrTvPG3TrrmlIZBM552uak9+687yB7856gzx31luRhunu0nTn5LWtt3RfW3fWAfjuorwW5JbXLoiWQRAEQRCVQRAEQTDn3UTLY+WOclTCKGmhPdq87Th+cDJn+NCMBlgcVD+9Z1Fn4qvcpmUuTSMf1J34KqnjV6fn1b7x+c37qt0bXz88Gc1h3XneYOu487xB4s7xBr476w3y3A2Tv6vnLk33RrmrdW906C59Q9tzF+W1PEdmee2CaBkEQRAEURkEQRAEURkEQRAEzPkzg5Eq31op+vCWkg9IHP7W5OMZqw9NlpdGk2+gDqRpFkS7nDdLZC7e+ernnh4+TbeYPNm8WgffXK6ee80bVN153qBbd7P25eacz/MG1XR73sB3Z71BnjvrLU2DJU13l+5yr+G27qwD8N1FeS3ILa9dEC2DIAiCICqDIAiCYO67ieDelaJttnNQbaOtmGFsqw9PhmnJeLI9fTMwh/SjLG2Z5Xy1NxrH0/NqHax5mrZu3Xne0njmwZ3nDXx3qcccdzaeNA25dOlu1nPluFtJht567qK8FuSW1y6IlkEQBEHQb2UgIueLyJdE5BYRuXTKfhGRPyj3f0FEnpobNgiCIMint24iERkCbwfOAw4A14rIflW90Rz2IuCc8ufpwDuAp2eGZUzxFjLASvr25rJ96l8ZatBF9h5ZqJ08a7JsHaR+ls2kWnaf6y2JZy5wvIHvbjmZjCzL3bx5g6xrDnx3UV7XFvPKaxcctWUgIpeIyMmdxwznAreo6q2qugy8H7gwOeZC4M+04DPASSKyNzNsEARBkElON9EZFHfeHyi7ZvzBvMfGPuB2s36g3JZzTE7YIAiCIJOjVgaq+ssU3TTvBH4K+IqI/FcR+c6WcU+rVNK2j3dMTtggCIIgk6wHyFpMt/f18mcVOBn4oIi8rUXcB4CzzPqZwMHMY3LCBkEQBJnkPDP4jyJyHfA24O+Af62qPw18L/CjLeK+FjhHRM4WkSXgImB/csx+4CfLUUXfB9yrqocywwZBEASZ5IwmehTwI6r6VbtRVcci8uJZI1bVVRG5BPg4MASuUNUbROT15f7LgKuAC4BbgIeAVzWFnTUtQRAE252jVgaq+paGfTe1iVxVr6L4h2+3XWaWFXhDbtiUAZMJrxaT596Dpcn3UsV+XELM8rw8hTB5snm1DlI/dqIwu8/1lsQzF+4cb+C7SydYy3Inicc5dmcdgO8uyuvaYl557YJ4AzkIgiCIyiAIgiCY84nqhgInLhb13drvNRZ3TrK+sGvH+rIOJttH1Tm1shgMhkc/aIPPN0pfDF6YnlfrIPVzeDyYus/zBvPnzvMGvjvrLd2Xc81B/+5mPVeOO+sAfHdRXgtyyyvVT0vPRLQMgiAIgqgMgiAIgqgMgiAIAub+mYFw8mLRh3dKMqRt58k715cXjpss63BxfXncMDOgVEa3Dacup+u531f1zlc/9/TwabptnmxerYPUj51B0u7zvKXxtHWX5rVLd543qKbb8wa+u3TW0hx3Np40DZY03Tl5beutvs8/R4476wB8d1FeC3LLaxdEyyAIgiCIyiAIgiCY826ipYGwb1eRxROPrw4NPO5Ru9aXB7tPmOxYWFpfXEk/3mKwM3kPTJi0adgWez4bT5oGSy3dJpzNq3VwyglVP0NzauvO9ZbE80h21zQLeyXdjjfw3Q2TU2e5S/6unrs03RvlLj1Xl+6sA/DdRXktz5FZXrn7WFNaJ1oGQRAEQVQGQRAEwZx3Ew0XBpxyatG0Ou7U4yr7dp564vryYM9J68s6nDTRRg2jCQZmUq3qCIJq/do0usDDO1+t+T6Y3uysvdFo8mTzah0cv/dblTDDpUm81p3nLY2nrbumUR5N5JzP8wbJW7SON/DdWW+Q587GU6Rhurs03Tl5best3dfWnXUAvrsor2WYzPLKrVlJbSRaBkEQBEFUBkEQBEFUBkEQBAHz/sxgccAJZxZDs9IhbbvPOGV9eXD8SevLo4XJkK2V8QPuucXpg0yHkw0WJ+v2jcb07cbKOUyYpmFw4vRBpkPVdGHS/zo0ebUOTjjrnkqYhV2TS8O687xBt+6sA/Dd1fplM9x53op0T9x53sB3Z71BnjvrrUjDdHdpunPcpdeZ587zlh7X1p11AL67KK8FueW1C3ppGYjIKSJytYh8pfx98pRjzhKRvxaRm0TkBhF5o9n3qyJyh4h8rvy5YHNzEARBMF/01U10KfApVT0H+FS5nrIK/CdV/S7g+4A3iMgTzf7fVdUnlz+Nn78MgiAImumrm+hC4Dnl8ruBTwNvsgeo6iHgULl8v4jcBOwDbsyNZLhjyImPLYZj7Tjp+Mq+XadNGiPDE09dXz5s5oxaGTVNfGXeaFz0m4b2YxfjzGFrA+e4tOvEbXYm6V4xq0smr9bBnn2n2iAs7r5/fdm687xBt+7Sj4R06a6xq8Ok2/MGvjvrDfLcHU5Uee7SdOe4G9e6Kqa787zV42nnzjoA312U14Lc8toFfbUMTi//2a/90z+t6WAReRzwFOAfzOZLROQLInLFtG6mIAiCIJ8NqwxE5JMicv2UnwuP8Tx7gA8BP6uq95Wb3wF8J/BkitbDb3eZ9iAIgu3GhnUTqeoLvH0icqeI7FXVQyKyF7jLOW6RoiJ4j6p+2Jz7TnPMnwAfnRZ+sLjInn2PBmDHSXsq+xYfdfokrTsm+w6vmqbu2G92DpyJr9KmYWWfHZ0wSkYnDI8+MqQ28sGd+Kqabpun40xerYM9++6thFncPZk73brzvKXxtHVXy6vjznrLPZ/nLU235w18d9Yb5Lmz8aRpsKTpzsprOprIcZd9Dbd0Zx2A7y7Ka0Fuee2CvrqJ9gMXl8sXAx9JD5Biir93Ajep6u8k+/aa1ZcC129QOoMgCLYFfVUGbwXOE5GvAOeV64jIY0RkbWTQs4BXAs+bMoT0bSLyRRH5AvBc4Oc2Of1BEARzRS+jiVT1HuD5U7YfBC4ol/8WmNquUtVX5sQzXFrg+O8omlaLe3ZX9g1OnjyzHu+czBm+bEdEpDNI2fALk3p0WFlOm52TT9gNbbNz0PASiw1jzmfjSdNgSdNt82Tzah3sfsy3K2GWTpj4su48b2k8bd1ZB+C7q8+9f3R3nrc03Z438N1Zb5DnbjkdTeK4S9Od426YdhM57jxvaTxt3VkH4LuL8lqQW167IKajCIIgCKIyCIIgCOZ8biJZXGTp9OJZ82BndX70oWlyjXZMmqTLq5Mm21gbRieYF0iGQ9PsXKrOqWJHFFTnOklfBhpMDWPPZ+NJ02BJ071smqFq8mod6IP3VcLI7ocm8Rh3njfo1l06EsNzl85Hn+OuaU5+m27PG/jurDfIc2e9pWmonCtJd467+txE09153tJ42robJt1Enrsor2W8meW1C6JlEARBEERlEARBEERlEARBEDDvzwwWFhmeegYAg53VPl92n7S+OF6a7FtdnvTXNb3RKJU3Gqf3H0K386OnQ9Mk841G2yVt8zo0Doan2vf4QA4/OInXunO8Qbfuuv6egY3H85am2/MGvjvrDfLcWW9pGixpunPcdfE9gy7dWW/gu4vyWpBbXrsgWgZBEARBVAZBEATBvHcTDRfXh2NJMoRstGMyX/qKqROXzYRUzfOjT5YrQ++S7o0FE69mTnxlw9jzpUPVxKnK03RX3tI0eR0aB8MTH1U9965J89S687wV8XTnbiH5e3nu0onqctx53tJ0e97Ad2e9QZ675eRa8L9nUF3PcVfrJnLced7SeNq6s97AdxfltdyXWV67IFoGQRAEQVQGQRAEwZx3EzEYro9CGC9U55m3E0BV50TPe6Nx6Ex8VR+JMb35Pk6a74OBMz96w8RX6bqXbpsnm9cl40BGK5Uwsrhjcj7jzvOWxtPWXerRc5d+HjPHnectTbfnDXx31hvkubPxpGmwNP39vXyn3W2euyb3XbpbSib889xFeS3ILa9dEC2DIAiCICqDIAiCYM67iXQwZLzzxGI5aQ6OlyYTYR15aHV9+bB546NpfvTKSyzDyfLCYrXbYrRj+ugEaXiJZWjC2PPZeNI0WNJ02zwdsRN7HTdxIKPl6rlXJ012687zlsbT1p31Br679KWzHHeNL06NbBN9ujfw3VlvkOfucHJuz13tpbMMd7WXpRx3nrc0nrburDfw3UV5Lcgtr10QLYMgCIKgn8pARE4RkatF5Cvl75Od424rP2/5ORH5x2MNHwRBEOTRVzfRpcCnVPWtInJpuf4m59jnqurdM4WXAeMde4rlYfUzirb5tWzmBrHbG95hqcxNXpkrvfapu+lznY9Xl93jvBEJ6Xzo3vzoabpz8rormXtHh6aZbtx550r3tXVXG9HiuGsaDeK5a5qT36Y7N6/WXcUbZLlLu6A8d01/f89dOl+/565pFEyX7tK8uu6ivAL55bUL+uomuhB4d7n8buCHNzl8EARBYOirMjhdVQ8BlL9Pc45T4BMicp2IvG6G8EEQBEEGG9ZNJCKfBM6YsuvNx3CaZ6nqQRE5DbhaRG5W1WtyA+tguD4KYTVp5tsn9nYuELu96SUWsc1O+0LLMH3RZKJYx5PmZDqnTmV0gglTmUclnRI38zN6bl7N8nCxeiksLE2a6dadd650X1t31gH47mqjiTLced7SdDfm1XFnvUGeu3Q0kecuTXeOO+sNfHeetzSetu4OJx49d1FeC3LLaxdsWGWgqi/w9onInSKyV1UPiche4C7nHAfL33eJyJXAucA1QFb4IAiCII++uon2AxeXyxcDH0kPEJHdInL82jLwQuD63PBBEARBPn2NJnor8AEReQ3wNeBlACLyGOByVb0AOB24snxRYwF4r6p+rCl8yliVh1eKJlf6xL4yTex4+vKoaa4TOyKhoWk4GE4f5dH45STnfLUmrTs6IZ3rZHr+rIOhJM13sR4m2z1v6Xpbd4NaV8V0d7UvnWW487yl6fa8ge8u9ZjjLj235y5Nd467dLSV+6Wzhmu4S3dpd5vnLsprfbmpvHZBL5WBqt4DPH/K9oPABeXyrcCTjiV8EARBMBvzPR2FwpGyNh3VxombBzMr019pT8N4SGXccrX2X1ia3EGouQPQcfKqujmHDWPP1/TwzpKmuzJNgMnrTntHQ/Uhpr2LGVXGOk/3lsbT1p11AL671EmX7jxv4LtL7/5y3KXTEXTpTpO7Ts+d5y09rokcdzvTFp/jLsprQW557YKYjiIIgiCIyiAIgiDYBt1Eaw9dmh7SVGY+tA+kGpqdtklrXzNPZya0D5HUzGioybnFecBVmW0xfYDoPZBqeLDr5XWYtDqH5hTeg8HabJsduksfvnnu0qZ4jrvGh6DOw7umvFp3wyTbOe5qD5Add2m6c9xpMiun587zlsbT1l2aV89dlNeC3PLaBdEyCIIgCKIyCIIgCOa9mwi/m2i10qSdtLlWM0cnVJqd5iMW6SyIq2Y0gG1OjgfVcw9k+iiEyiyIw9manTZPlbxWxjBXz2Gjsu48b2k8bd2tJqN3PHeDpJmf4y63q8PzBr675E+U5W41czRRrZsow13a3ea587zV4mnpLp1mwnMX5bUgt7x2QbQMgiAIgjlvGaiuP3RJ7zTs3OAr5s0+++bjLA+k6hNfTfbZscpD/DssG6bytuSMD6RsnmxerQOR5A7SuUvzvKXxtHWXjv/u0l3u3a3nDXx344aWQc41l6bB0vQA2XOXjo/33HneavG0dJd+z8BzF+W1ILe8dkG0DIIgCIKoDIIgCIJ57yZi8tAlbeZ743fTB4U52AdITePe1dgeJ01Dr+nadO5cbJ68Mczpg1g7PN26axoz3qW72nsGjrtaU7xDd5438N0lw/qz3M3iDfLcaVLCPXeet2nrOeRcc+C7i/K6tpxXXrsgWgZBEATBfLcMxjp56JLeQVRqXzOUy94B5D6QEmeYWbpuh5qlz3+8c4gTT5oGS5pum6cVZ9jakWSo2lgHU4/zvKXxtHVX+6qX4y51kuMu9yGo5w18d9ZbelzONZemwZKmO8ddOrzRc9fkvkt3aTn03EV5Lcgtr10QLYMgCIIgKoMgCIKgp24iETkF+F/A44DbgH+nqt9KjnlCecwajwfeoqq/JyK/Cvx74Bvlvl9S1avSeFR1/aFL+tHpI95kV5njli1N45bH9oFU5XwN45btmPGGccsejeOWK/Prm7ctkybtyDRJx95Y+YZ42robpw+Qe3DneQPf3Sjp3shxl/ueQUqOu3SCNc+d5y2Np4kcd+l7Bp67KK8FueW1C/pqGVwKfEpVzwE+Va5XUNUvqeqTVfXJwPcCDwFXmkN+d23/tIogCIIgyKevB8gXAs8pl98NfBp4U8Pxzwf+WVW/eiyRKJOHLulNg6197Vwg6R2Jx4L30Ch90GQfSC34d2zuQ6jB9GPSNDRh81SZy0UnY/nSO9+B+caq3eV5S+NpIsdd7QGy467pAaB3vrbewHc3SL5Nm+NuFm+Ql9f0G7+eu9xruMtrDnx3UV4LcstrF/TVMjhdVQ8BlL9PO8rxFwHvS7ZdIiJfEJErROTkjUhkEATBdmHDWgYi8kngjCm73nyM51kCXgL8otn8DuA3KG7+fwP4beDVaVjVycsr6R1E5duplbu3vKFqHmk/YeVOw8x1Mk6qYW8WxNx+R0u9D9KbM8b2Qfrpse48b7V4WrqrtQwcd02zlrZ153kD312anhx36Tw8XbobJHMTee7aeoM8d+kQXc9dlNe15cn2pvLaBRtWGajqC7x9InKniOxV1UMishe4q+FULwI+q6p3mnOvL4vInwAf7SLNQRAE25W+uon2AxeXyxcDH2k49uUkXURlBbLGS4HrO01dEATBNqOvB8hvBT4gIq8Bvga8DEBEHgNcrqoXlOvHAecB/yEJ/zYReTJFN9FtU/YDoEymsK41O+3bki2bmvbNwtWGaYbVDmlrGKrmNfmb3v5sYuTktfpN1fQB8mTZC5M67dJd2tzuw53nDXx3aTQ57mbxBnnuNEmQ566pi65Ld/VvIE93F+W1ILe8dkEvlYGq3kMxQijdfhC4wKw/BJw65bhXbmgCgyAIthlzPTdR8QB5+qyGlbuLzOFplmHmHUDTPCg5Ybw4jxavh81r0x3WiOlO2nqDPHdNcw41keOurTfw3XneamFaXnPT1tfo8ppL4+nymoN+3M1jee2CmI4iCIIgmPOWAZPaNB0aaGcG9GY+nKX2rd/RTpYHmnmn0TArZw61u3wnr5XZEZOXpaofJ58se+HTeNq6S18G6sOd5y1dt+7SIX857pr+Xrl47jbLG+S5Sz167qK8FuSW1y6IlkEQBEEw3y0DmNxh1Poq1VluOTohHQVTGZ2Q+VGmgXO+LkYnePke1Pphp78A5IVP48nFc1cbTdSDO89bul5157901uU1B3nu2npL48kl55oD312U13I5u7y2Z64rA1WtzSmzxrjhoVYO7sO7xvlj8uLJ/XTeLBebl+/064HjjAfIs3iDPHd1j925a+stXbfuPG+1MB1ec9A0V84j95qD/t3NS3ntgugmCoIgCOa8ZUC9WbrGyBmqNssDqdyharYJ2fSB7dyhah5ND6S8fOc+LPPC1+Jp6S514LmrzS3ToTvPW7re1t2sD5Bz3KV+PHe5Q0ubyHGXeuzSXZTXdkTLIAiCIJjvlgH4/YtpTd8V6d2A/W51ZXbDJFyX/du5VIatZQ5V2yhvUM1r+r1vz13XfbS5bBV3tdlfG/ZNO1fX1Ibo9uxu3svrsTD3lcEa9Wa+WW45VrkJ25wcmUib/onNOoWwh9t8r4yprua78jlCb0RMB+PjPVIHfbhrui48d7XPh2a426xrDnx3fVxz4LuL8jpluaG8dkF0EwVBEATz3TIoHiAXNWitedphzdo078mqWbYPmjSJf6Pm1GmicaiauU2oNE87viPx8reaHOe528g5dZpw3SW3V327S/3kuOtiTh2PpqGl3jU3LVwb5rK8dsBcVwZoXl/jbC+u2FKf9nBPqDQvx3n/xHInyKqmIY9KXof+cRvlDfLc1Rx06K61N3Dd5fZtt7/mIMvdOO+f2Fa55mrny2Tey2sXzHdlYGj6RGNl+wY+5MsdqtY1Xp6ahqp588Q0zRjZh7s+vIHvrmluor6vOejfXdPQ0qa5ifp290gvr10w15VB0U109ONc+S1fdW8i92JqOxXAseyrHNfC27HEY3kku+vS29HO17e7LqZRyNleO66lu769Hcv5LF1fC7My15WBpev+WsuCuQCWk33ekD9Nm+8ZfY0LG3g3kvpp+jh5l3jumob8WXe5X+XaLHeDpDuhb3dph4jnrumfWB/uorw2sxF+ehlNJCIvE5EbRGQsIk9rOO58EfmSiNwiIpea7aeIyNUi8pXy98neOcaqU8WNxrr+s11pcrDmbdrHSLa7N/A9WG/hro510OSuKdx2ZaMd9DW09HrgR4BrvANEZAi8HXgR8ETg5SLyxHL3pcCnVPUc4FPleiMj1cpP38hAKj990+TnkeQNeER5g2Y/4a6ZnGvukeBuK5XXWenrG8g3wVE/BHEucIuq3loe+37gQuDG8vdzyuPeDXwaeFMtHnxR7osdLWvd3GF5aTzekLQuhqfl5LXWLXOM3qatHyu5+W5Kd5fucvNa6VrIfMDe9YtTbd31cc2lcfXhbl7Kaxc8kp8Z7ANuN+sHgKeXy6er6iEAVT0kIqdNO8HtN19/98888/Ff3dhkBkEQ9M5j255gwyoDEfkkcMaUXW9W1Y/knGLKtmO6DVDVRx/L8UEQBNuVDasMVPUFLU9xADjLrJ8JHCyX7xSRvWWrYC9wV8u4giAItjWP5LmJrgXOEZGzRWQJuAjYX+7bD1xcLl8M5LQ0giAIAoe+hpa+VEQOAM8A/o+IfLzc/hgRuQpAVVeBS4CPAzcBH1DVG8pTvBU4T0S+ApxXrntxTR2eupUQkStE5C4Rub7vtLRBRM4Skb8WkZvKocVv7DtNsyAiO0Xk/4nI58t8/FrfaWqDiAxF5J9E5KN9p2VWROQ2EfmiiHxORP6x7/TMioicJCIfFJGby3LyjE2LO52AaZ4oh6d+maLCOEDR2ni5qt7Ya8KOERF5NvAA8Geq+q/6Ts+slF16e1X1syJyPHAd8MNb8O8hwG5VfUBEFoG/Bd6oqp/pOWkzISI/DzwNOEFVX9x3emZBRG4Dnqaqd/edljaIyLuBv1HVy8sekeNU9dubEfcjuZuoC9aHp6rqMrA2PHVLoarXAN/sOx1tUdVDqvrZcvl+ihbfvn5TdexowQPl6mL5syXvqkTkTOAHgcv7Tst2R0ROAJ4NvBNAVZc3qyKA+a8Mpg1P3XL/fOYREXkc8BTgH3pOykyUXSufoxi8cLWqbsl8AL8H/AKwAZMibyoKfEJErhOR1/WdmBl5PPAN4E/LbrvLRWT3ZkU+75VB6+GpQfeIyB7gQ8DPqup9fadnFlR1pKpPphjldq6IbLnuOxF5MXCXql7Xd1o64Fmq+lSKGQveUHatbjUWgKcC71DVpwAPkjG7QlfMe2XQNDw16IGyj/1DwHtU9cN9p6ctZTP+08D5/aZkJp4FvKTsb38/8DwR+fN+kzQbqnqw/H0XcCVFF/FW4wBwwLQyP0hROWwK814ZNA1PDTaZ8sHrO4GbVPV3+k7PrIjIo0XkpHJ5F/AC4OZeEzUDqvqLqnqmqj6Oomz8laq+oudkHTMisrsckEDZrfJCivnPthSq+nXgdhF5Qrnp+RTT72wKj+TpKFqjqqsisjY8dQhcYYanbhlE5H0UczE9qhyS+yuq+s5+UzUTzwJeCXyx7G8H+CVVvaq/JM3EXuDd5Wi1AcWw5y07LHMOOB24spzrbAF4r6p+rN8kzczPAO8pb15vBV61WRHP9dDSIAiCII957yYKgiAIMojKIAiCIIjKIAiCIIjKIAiCICAqgyAIgoCoDIIgCAKiMgiCIAiIyiAIOkFE/o2IfKH81sHu8jsHW26+omD7Ei+dBUFHiMh/AXYCuyjmmPlvPScpCLKJyiAIOqKcQuBa4DDwTFUd9ZykIMgmuomCoDtOAfYAx1O0EIJgyxAtgyDoCBHZTzEV9NkUn/e8pOckBUE2cz1raRBsFiLyk8Cqqr63nM3070Xkear6V32nLQhyiJZBEARBEM8MgiAIgqgMgiAIAqIyCIIgCIjKIAiCICAqgyAIgoCoDIIgCAKiMgiCIAiIyiAIgiAA/j9o5hmUmfF9JQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tree_result = tree_op.evaluate()\n",
    "tree_result.require_grid_space\n",
    "plot_bot_2d(tree_result);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Deferred evaluation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A key point is that the operator objects symbolically represent an operation on the field arguments, and are evaluated using deferred evaluation.  If we change the data of the field arguments and re-evaluate an operator, we get a new result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set scales back to 1 to build new grid data\n",
    "f.set_scales(1, keep_data=False)\n",
    "f['g'] = np.sin(3*x) * np.cos(6*y)\n",
    "plot_bot_2d(f);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tree_result = tree_op.evaluate()\n",
    "tree_result.require_grid_space\n",
    "plot_bot_2d(tree_result);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Differentiation, integration, interpolation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In addition to arithmetic, operators are used for differentiation, integration, and interpolation.  There are three ways to apply these operators to a field.\n",
    "\n",
    "First, the operators performing these operations along a given dimension of the data can be accessed through the `basis.Differentiate`, `basis.Integrate`, and `basis.Interpolate` methods of the corresponding basis object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's change the data back to our first example, with a constant offset\n",
    "f.set_scales(1, keep_data=False)\n",
    "f['g'] = np.cos(4*x) / np.cosh(3*y) + 1\n",
    "\n",
    "# Let's setup some operations using the basis operators\n",
    "fx_op = ybasis.Differentiate(f)\n",
    "int_f_op = ybasis.Integrate(f)\n",
    "f0_op = ybasis.Interpolate(f, position=0)\n",
    "\n",
    "# And we'll just evaluate and plot one of them\n",
    "fx = fx_op.evaluate()\n",
    "fx.require_grid_space()\n",
    "plot_bot_2d(fx);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Second, more general interfaces taking bases as arguments are available through the `operators` module.  The `operators.differentiate` factory allows us to easily construct higher-order and mixed derivatives involving different bases.  The `operators.integrate` and `operators.interpolate` factories allow us to integrate/interpolate along multiple axes, as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total integral: 12.566370614359172\n",
      "f at (x,y)=(0,0): 1.9999999999999727\n"
     ]
    },
    {
     "data": {
      "image/png": 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dZFSWKbegzqXniuocZMa6/aisWevcOF1Z1F2vf3qdq86ZYp06B9FeId9e+2DIdwYXAY+Y/cP1sQlEZBdwJfDb5rACHxeRL4jIz2yalUEQBGcAQ3oG017we/3d3wD+OBkieo2qHhGR/cAnROSrqvrpNONq3bOmhbXiv83x0rXl2ydyccvm6WS84qYTE7is3pK4Hdcmaj19TTdtXadp5+xde7ql5bSulZtO6t1f6k042kky0aBP7TzdUvOsdhMzkM12lzqXpUC7lm5JuqI6N21/Lf+MdQ587aK91peYbtpEe+2DIT2Dw8AlZv9i4IiT9hqSISJVPVL/PgbcRjXsFARBEHRgSM/gLuCgiFwKfIPqH/7fThOJyDnAjwJ/1xzbDYxU9al6+03AP03zKs2Y2ygzLtset2zFA5TdSelqm61x3dV2ulbYSdnTcintlQ+Zuj0ZTdQcGDnjspPvGXrULhv/bbSbCDvpTztPt3S/HRHTTlii3eTaNP6Kr4mBZtu773RM3NGu8Gm5lJI6l17aq3O5a0R77Y/BOgNVXRGR64CPUYWW3qyq94rIz9bnb6iTvhX4uKo+Y7JfCNwmVUNZBD6oqr+/ddYHQRDMF4POM1DVO4A7kmM3JPu/AfxGcuwh4PtPXQCsrnXUo3ZXutrqZac/UWQ738JIlda4o3m60HStE7stdqxyybfHWUFSM5Z7447pE+2qNc9oV6JbauvE+GiBdhNj3Y52qQVF2k2sQHlq7XJj3Va71fTWZtSufaIsUsWrc9Ulpmvn6TZhj1PnqnSn1i4d63a1i/ZanStsr30QM5CDIAiC6AyCIAiCOV+oTlFO1u7dOHEtR8ZNa03myLyEcsPBCidL6cpJky5x30fNt1PFbGeX2y1k3NqeHsp3cjV1y61L2mji6VbtO+57aWhp5l497axu0K92nm7gazc5DHJq7TrVOSjSrqUbuNq5uqXlFFJS58DXro/26jKH7bUPwjMIgiAI5t0zKJsir4XL43pPuNmFwewThX0qW20/abSubPNkptRnX9LadAVhkLkXe97x9EXezIuGtYxLQvkc7Sb+IgXaTQRyOobnF/Lznmhzk4n6q3NQqF36ROtp5+iWltNnnYPN1c6zbx7bax+EZxAEQRBEZxAEQRDM+TBRdp6BfYfkeFzZNWMKV0G08cktV3Psu5DFL6GcuOW8u91stzUonGdQoNupzpVol8Z1e9pNFFOiXWaegT881t73tMvOM5hVu9K64NU58LWbsc5BmXapPsXzDDq015Z926y9trIX1oVce+2D8AyCIAiC+fYMFNZDS9N+b2yePHIvuMoKMrM6J540nCfalROtdLK4bNKZl3z2SaxrqJqzMmTuifZk60mo0c7TLb1eMd53CiZeIE/XrqUb9Kqdp1t6zmp3Mg1VLNCu81NeiXbpE62nnaNbZWt/2uU8UK/Owfy119yXCbu01z4IzyAIgiCIziAIgiA4A4aJ1l7AZOOb7Sy/WWc05pYMzrjvbrrCj2VkzbPFmL1cjPfYc08d3apyetQuM8+gpV0u3YwfGvF0A1+7yaWuT61dJ92gTLvMcFtRnZu2X5ONlbdFOnUOfO36aK9FKwbMSXvtg/AMgiAIgugMgiAIgjkfJrKULrdgSb9A1XI7C11AG6s8ESFj09lzueUW2pmmHy50IUunt3dxT60Npd8zaCVJ4uM97SaOl2iXi/LYZtq1T2yvOjfxPYMC+3LDP7njXdpr6062mXa2TfRd57oyqGcgIleKyAMickhErp9y/rUi8qSIfLn++aXSvEEQBEE5g3kGIrIAvB+4AjgM3CUit6vqfUnSP1LVt3TMGwRBEBQw5DDR5cCh+hOWiMitwNVAyT/0srwKq3WIwmihY8SGvVxuXf6NXitxQWW0vV7frJrQjlm161M3aGvXh2592reahBP1Ue/6pG/t+qTPOgfbu7323Sb6YMjacBHwiNk/XB9LebWIfEVEfk9E/uoG8wZBEAQFDOkZTOsa07ciXwS+S1WfFpGrgP8EHCzMGwRBEBQyZGdwGLjE7F8MHLEJVPU7ZvsOEfm3InJBSV4ABBZG3d0xyblyMptTJcnnGjtepNm00Ts9uKCz6HZKG4bWLlP+rNrNqlvWhhl1qy7Rn3ZplNjQ2m3rOpexoY/22gdDDhPdBRwUkUtFZBm4BrjdJhCRF0qtlIhcTmXv4yV5gyAIgnIG8wxUdUVErgM+BiwAN6vqvSLys/X5G4D/AXiXiKwAzwHXaBWUOzVvWoYAaw8bC0nvu2ReAI3MqFOuj3ant9seP+n9Zcmsbmg+sD0REW0/sG3zZK5tya2CaM/Ye7UanJTUombfaufplpZTjHN/LQ3A1S59Yuuinft5RLOd3quvXftaJdp1qnNQpp39qDu+dq5u0/bXrjXxRGu8U3PUq3Pga9dHe3XZBu01a57ZLm+vszPopDNVvQO4Izl2g9n+NeDXSvMGQRAE3dhesWVBEATBIMz1chRC41otJN3ekoljth7pqMvLHOMOaup2Li4158y2jJMXUsYFbOXpwe209yTGvbQaLI3b9z0y+1Y7T7e0nGIc7awGkNFulNF7xiE2TzfwtRslOpZol9MtG49eoJ0mOnraubol5ZRSUufA1y7aa32JwvbaB+EZBEEQBNEZBEEQBHM+TDQSYddS5d5NuJ3GzVsy8c0LLRe0naflsltXc9TImA5v2JUKR2fZw+1VFFvT2xd3mG3jgo6SP5cT853abe/J3qtqk39XYrb9xmprqMPRLS0nGzJeol2yyqSn3cSyACXaZdx3a7enG/japd+mLdEuXXnB1S6xu0Q7q1t1ytHO0S0tJzfPoEQ7qxv42vXRXltss/Zq6aO99kF4BkEQBEF0BkEQBEF0BkEQBAFz/84Adi9P7+8WzVicHZdbXPDHci2t8cAFG462s53OjrGmY4g2nd2245gLzexGXciM5RpSu+09LZuC7CuQhXHZc4GnW1qOtSEdWy7RbiLkz7nXiXnTBdqluln7rN2ebtCvdovJH8yrdxN/7wLtZq1zkNeuZU6BdmkkaJ/apbq1viZ2hrbXjRCeQRAEQRCdQRAEQTD3w0TCrqWqv0t7PbtsbDv8zx5PFmKzwx12gbTFxjVMP7st1iVdMvnTD3S3Zi6acDLrWi4mi7cZG9S5HwBbrP2LL5pZjOlHua119nKebuBrl86ilQLtJHWxPe0mZssWaJcsbudp5+kGvnbp379Eu4kQXbPv1jko0q6lG/jaebol5Xh1rrK72S6pc+Br10d7bbHN2qsltbtLe+2D8AyCIAiC6AyCIAiCOR8mWhjBOTumu2aeR9laSzxxg7V10ki35MxGJIl2KXXtCr90NbGgWE26FryVYNkJVRkXmpbzxHPaWbRAuwlzetTO0w3a2pXoBrNrlx622rl1Dsq0m1U3OG20i/Y6G+EZBEEQBNEZBEEQBAMPE4nIlcCvUH268kZVfW9y/u8A7653nwbepapfqc89DDwFrAIrqnpZev2Rjjnr5FNO4Y7ra9/4J27d2EQarDA9/2oalWMDEqZbMmmaDSBpLf6VROWY7UW7UN14pZVuwUZCjFdNOeZ4Gi3hGpcZMnC0GyeRQSXapW5wn9qljrennadbVU6P2qVRJo52K/jDDp52s+oGvnaL6UJ1BdpJqlWf2kV7nYnBOgMRWQDeD1wBHAbuEpHbVfU+k+xrwI+q6rdF5M3AvwN+yJx/nao+tmVGB0EQzClDDhNdDhxS1YdU9QRwK3C1TaCq/1VVv13vfga4eIttDIIgOCMYcpjoIuARs3+Y9lN/yjuB3zP7Cnxcqu/C/T+q+u/SDLJygoVvH653kn5vwUyeseuJLDWLmI937Glfz0QkrBh/8rmVZvv5lbb7ZndzwyCee7lozN652L6HsxbNhBtzTlZPtq99/Onm3MnnTLoTxrj2MIg7OcnRDXzt0jVeSrRLZHS1yw1peNpZ3cDXztOtSudol5ucVFDnwNduJak0JdrlhkFK6hz42i0kCUu0a+kGvnbRXqtzpe21B4bsDKbFTE0dphOR11F1Bj9sDr9GVY+IyH7gEyLyVVX99CbYGQRBMPcMOUx0GLjE7F8MHEkTich/C9wIXK2qj68dV9Uj9e9jwG1Uw05BEARBB4b0DO4CDorIpcA3gGuAv20TiMiLgd8B3q6qf2qO7wZGqvpUvf0m4J+mBeiJ51j52j3VThKxMTprd7O9d19T5t7zm/xpdMLyrvXt5803+p4+0Ww/8Xw7MuDJ483+sycb12418Tvt+iRrn+oEOGdH8yfatzNZetnYZ5IhJ55tpRs9/2Sz89R6f8r4qSea7eeeaeVpRc8Y7TzdwNfO6gZl2lndwNcuXdelRDtJ/q6edp5ukNEuiToq0c7qBr52zyff1CzRzuoGvnaebuBrlyQr0s7qBhntor1WlLbXHhisM1DVFRG5DvgYVWjpzap6r4j8bH3+BuCXgPOBf1svVLUWQnohcFt9bBH4oKr+/gC3EQRBMBcMOs9AVe8A7kiO3WC2fxr46Sn5HgK+f9MNDIIgOEOIGchBEATBfC9Ut/rcczx1z1cAWFhqz4Jd3teEoS2cf2B9e+lFzTjhKPkknh19PW7C0x5/rgkN+/Mnn2/lOfbM8fXtbz3dhIadSELalk2o2Xl7mtC5/bubhbRefE7bnmUTYifm+3ijJAySJ4+tb5488vD69urjRxt7nnja5mD1ZHNPVjtPN/C1S4PgSrSzuoGv3XISvlei3XISEutq5+gGvnZWNyjTzuoGvnZWNyjTzuoGvnaebuBrJ8m3QEu0s7qBr12014rS9toH4RkEQRAE0RkEQRAEcz5MtPLM8xz7fBWRurCz7Xbu2n/u+vbZlzauoiw3rt3iOftbeewnCE+sNtvHnmncyYceb4d8Pfho484dfaJxB4+faA8N7FhuwtMO7GtmVR68sHGP0xmN559lPtFnFxNbabu+K4/9RVPuI19b3/7O1xq389lj327lWX3euOxGO083yGtnKdHO6ga+dlY3KNPO6ga+dp5u4GtndYMy7axu0NbOq3NQpp3VDXztPN3A127ic6YF2lndwNeuj/Zqmff22gfhGQRBEATRGQRBEARzPkx04tmTHPlC5XIt72m7nXsPNO6gmtmJS/v2NduXHHSvbWc0Hnu6iUD46tH29xMOPdLMJnz6ycbtPPl82+1c2tm4nd95srmenfl4we52FMyl57YXOFtDTrSHBmwUwpOHvrG+/fj9zfZTR9vDMieeblx2q52nG/SrndUNfO2sblCmnacbtLXzdANfO6sblGlndYO2dnY4IZ2BXKKd1Q187TzdoF/trG7gaxfttaK0vfZBeAZBEARBdAZBEARBdAZBEAQBc/7O4PjJVR46Uo0J7knCvPab8cml3c345NmXNrMbdxxvrybYGr892YxBPvpUM2b49WPtsbxvm1C173yzWYFw5fl2usWdTUjayeeblRi/vqMZm0xD/qwNNgRRE7tPPP6txoY/b2Y3Pv5gE5527Fg7xO5pM+PSaufpBnntPLs97b6dhJZ62lndoEw7Wz742nm6ga/d08lM1RLtrG7ga5faXaKd1Q187TzdwNdOkg/nlGhndQNfuz7aq2W7tVdLH+21D8IzCIIgCKIzCIIgCOZ8mOjEWHn42cq93L3Q7vcWvtm4WXuPGff2O81xPd6eGWix30598tnGhX32O+0F1p761hPr208/2swmXHm+7eYt7mw+3iHme6979jUzLG05qQ2W1G57T8+Ye33caPC1Z9rXfsaE4lntPN3ScmbVzuoGvnZWNyjTztMttdvTDXztnknCP0u0s+WkNlhSu0u0s7qBr52nW1rOrNpZ3cDXbt7ba3tocvb22gfhGQRBEATDdgYicqWIPCAih0Tk+innRUR+tT5/t4i8sjRvEARBUM5gw0QisgC8H7gCOAzcJSK3q+p9JtmbgYP1zw8BHwB+qDAvKwrfqheYOrHYjnx48mTj2p0w65avPN9s60p7LXjr2p0cNy7fU+a7qSeSb/eefKaZ0Xj8qSYaII1OWD3ZlLXT5Dlx/IL17WeTxbKsDTbSKbX75DPGfTf3+qSJbvh28q1cG9lhtfN0g7x2nt2edlY38LWzukGZdrZ88LXzdANfuzSaqEQ7q1tqg1fnoEw7q1tV1nTtPN3A1y5dqK5EuyeTiBpPuz7aq2WI9vpUeu1NbK99cErPQESuE5FzT5WuA5cDh1T1IVU9AdwKXJ2kuRr4Ta34DLBPRA4U5g2CIAgKKRkmeiHVk/eH66EZOWWOMi4CHjH7h+tjJWlK8gZBEASFnLIzUNV/RDVMcxPw94AHReT/EpG/NGPZ0zoVLUxTkjcIgiAopOgFsqoq8Bf1zwpwLvAREXnfDGUfBi4x+xcDRwrTlOQNgtMeFVn/SVkQWf8Jth/277ORv5EsjNZ/tpKSdwb/i4h8AXgf8MfAf6Oq7wJ+APhbM5R9F3BQRC4VkWXgGuD2JM3twDvqqKJXAU+q6tHCvEEQBEEhJdFEFwB/U1W/bg+q6lhE3tK1YFVdEZHrgI8BC8DNqnqviPxsff4G4A7gKuAQ8Czwk7m8XW0JgiA40zllZ6Cqv5Q5d/8shavqHVT/8O2xG8y2Aj9XmjdlUeC8pSokLZ3ReM5Ss7+8p/kIxeLOZlsW2x+nsK760qjJv3dHI+PyjrakS7vPWd/esbcJylpYal/bzmi0eez1diXf+7U22BDE1O6l3c2sSHuvVoNzl9rXXh4192q183Sr7sHXzrPb085qAL526QzkEu1s+eBr5+kGvnZWNyjTzuqW2mBJ7bb35GlndQNfO0+3tByvzqV2l9Q58LXro71aTqf2au+ptL3SjmLtRMxADoIgCKIzCIIgCOZ8obrlkfCSXdXa5+n66Oe/oHHzdu/f1eQ52yxAtaO9YJdlp7neObua9dV3nb2jlW7vefvWt3X10vXt3ProNo+9ni0ntcEOYaV223uy92o1WNWy7xl4uqXlzKqd1QB87dLvGZRot3PRfwaydnu6ga9d7nsGJXUutcGS2l2indUNfO083dJyvDqX2l1S58DXLtprRWl7pf0Z5U6EZxAEQRBEZxAEQRBEZxAEQRAw5+8Mdiwt8NIX7QVgeU97/G7vgWbM7+wX71/fXj7/vPVt2dEeJ7bhYDtNmNeFe5txwu/an3yT93izuuDSziYczH43NT2355yzpl7PlpPa0LIzsdvek73Xk+YDGak+J56efs7TLS0ntcGz29PO6ga+dvY4lGmX6tYevzXj0Y5u4GtndUvPldS51AZLaneJdqk+nnaebmk5Xp1L7S6pc+BrF+21orS98tjUS2+I8AyCIAiC6AyCIAiCOR8mWt61xIt+4IUALOxsu1W79jezC8++9MD69sL5zbYun4XHTjNDcv+exh38Kwf2ttItmFmVR59o0h1PPlSzw8xWPLCvKffghY3bactJbbCkdtt7OucvP7G+bRfC2rW//RGU1ecbl9Rq5+mWljOrdgvJTF5Pux3JLM8S7TzdUrs93cDXzuoGZdrZclIbWkMdid0l2lndwNfO0y0tZ1bt0sXXPO36aK92+G/e2yufm3rpDRGeQRAEQRCdQRAEQTDnw0SLu3ey/7LvBmBhqe12Lu9r3Dnrli1e8ML1bV1szwy0bufyQrO9f3ezmNTz57dnWO7Z2Uj8Xec3UQMnkpmqy2Z24nlmcar9u3eY7faCVtYGO5yQ2m3vaceJ5vuq5+1q0u256AWtPKsnjctutPN0S8tJbfDs9rSzuoGv3XIyU7VEO1s++Np5uoGvndUNyrSz5aQ2eHUOyrSzuoGvnadbWk5qg2d3SZ0DX7s+2msr/zZrr5Y+2msfhGcQBEEQRGcQBEEQRGcQBEEQMOfvDBbOOou93/f91c6oHYI4OqsZKxzt3dec2NvMNBwv+eGROxab8b/zz2rGN9NvnZ5nzj17ThOetjpufxjEhrTtMh+uOMd8LGNfMo5ubbBjy6ndC+c0sxiXjA4L5zT3uvhcsgri2ITSmTyubtCrdlY38LVLQ1BLtLPlg6+dp1t1ztFu3A5BLNJub3t2q6ddaneJdlY38LXzdIO8dp7dJXUOMtrNeXu19NJee2AQz0BEzhORT4jIg/Xvc6ekuURE/lBE7heRe0XkF8y5fyIi3xCRL9c/V23tHQRBEMwXQw0TXQ/cqaoHgTvr/ZQV4H9T1e8FXgX8nIi8zJz/16r68von+/nLIAiCIM9Qw0RXA6+tt28BPgW82yZQ1aPA0Xr7KRG5H7gIuK+0EFk+i8VLv6/eSfq9hcb90oUmBEyNy6bLmYWvTJiYLjfXXhz5LvaqyZ94ndjRDuu62sjJ9OMmO71QtcTusTZhcWLudWRc7NFqMrxh8rS0c3QDX7v0W7kl2qUutqddMkpUpJ2nW2q3pxtktNN2CGKJdpoME3japXaXaLeaaO9p5+kG/Wo3SobEXO2ivQIbaK89MJRncGH9z37tn/7+XGIReQnwCuCz5vB1InK3iNw8bZgpCIIgKGfTOgMR+aSI3DPl5+oNXmcP8NvA31fV79SHPwD8JeDlVN7Dv+zT9iAIgjONTRsmUtU3eudE5FEROaCqR0XkAHDMSbdE1RH8lqr+jrn2oybNvwd+d6oNi8usnnuxY4T9HqnpE20UQ+KqquMO7llujp+VRAxY9zLxNF3sFVruaDIm4jrsC+1InPFZ5zQ7O5qZnGLd8nR4wzXO0Q1c7dJv5ZZol7rlfWqX6tYaxjLaebpVeXrULomc8bRLh29KtJtVN/C1S4f/SrSTVKs+tTuN2qtX56Dn9roBhhomuh24tt6+FvhomkBEBLgJuF9V/1Vyzq6D8Fbgnk2yMwiC4IxgqM7gvcAVIvIgcEW9j4i8SETWIoNeA7wdeP2UENL3icifiMjdwOuAf7DF9gdBEMwVg0QTqerjwBumHD8CXFVv/xeckRBVfXtJOWMZ8dzS3qnnUld4jbbL57t5i5g3/i2XLY0mMdupW+0hjnGausGjqedWR4nbaRdic7r/dFjGw9MNfO3SLEXapZl61G5ieIvp2pXoVqUrM62kzlXppmu3mNStIu1m1Q1c7VTaw1vjgbU7ndqr1W68ie11I8RyFEEQBEF0BkEQBMGcr020OoYnj1eTM9JeT4xrZ79Gt2T80eSLilhnTsYrzfbK8ebEyol2OSZdy+3MTU4ytqmdFLPYnvjEYrN2+thsp+uonFht9k+ac6s2OCGdnGS2rXaebuBr13aCy7Rr6VYZaLYzk5NKtFtsr9fvaefpVqWzppnJSW1rirRbSsZAPO1STYq0S4c6PO083cDVTpMoKDtJq6TOVeZN127e26vVLp0Y2KW99kF4BkEQBEF0BkEQBEF0BkEQBAFz/s5grMqzJ6fP1Fs0Y42tMVujSLqu1JI9YNdeN+OOo5PPtTOtmrHclfb3cT10sRnttAtVTdxJOra7VmQyvm3HHY+vTB+PXCmMVXN1A1e7xWTqrJRot5qM5fapnaMbtLXzdEvPzaxdYo7Vzq1zUKTdrLpBv9ql71761C5tr7beFdU5mLv2uhHCMwiCIAiiMwiCIAjmfpgInjlROWuTYZBmNqAJSbOu5moyDGIXvhrZULXVxp2UledbeeSkDWNrtnWczCYdWZfWhKAtmZmTqZuZhl+u2Z14kCur00P+2iFsbXtsGFs7lG+6bpDXziIF2rV0A1c7q1t17QLt0hBNE6ZntfN0S/etdmnoZIl26fCG1c6rc1Co3UpbR087T7cqna9dy+4C7VIdPe36aK+WkjoHW9devToH3dprH4RnEARBEERnEARBEMz9MJHy7MkqiiB1O3eZ6YliZhMuq7+mfgv7aTrrOqcRCMbVHD/3jDGu7eapcTtH9iuIxjZZbLvoam3IfKLPuqEnx9NdzTWd1vM4LrunG/jaTax7X6JdMrzhaafJMFGJdprMJrVDMWPHfU+jYDztcsNEJXWusoHpJHaXaNfSDVztPN3A1y79u1q7S+oc+NrNe3v16hx0a699EJ5BEARBEJ1BEARBMOfDRErjWo0TV/zkqHG/lkyXmLpslonhjvWCvLXSQVvue7OtyQQiMQtX2TxiF7fKfOqu/WnJ1H0366NbF9RGJ6ymrqoddmqu7emWluPblp6crp1OuO/TtZNksbQu2nl4uoGvXbroWIl2uTqXpUS7REdPO0838LWb/LvaOnPqOpfue3UOetZuG7TXHF3aax+EZxAEQRAM0xmIyHki8gkRebD+fa6T7uH685ZfFpHPbzR/EARBUMZQw0TXA3eq6ntF5Pp6/91O2tep6mNd8is2wsCPBhmbPlGnf2kzj3UHU7fz5AlzyriaaXRCyzizPsoO/9rF5pntsdlrTfjJRIbg5BknzxJ9amd1q05N127CWe5RO0838LWbjGg5tXaddIMi7dLhDVc7T7e0nFLTbJGOBpDTLtorlLfXPhhqmOhq4JZ6+xbgx7c4fxAEQWAYqjO4UFWPAtS/9zvpFPi4iHxBRH6mQ/4gCIKggE0bJhKRTwIvnHLqPRu4zGtU9YiI7Ac+ISJfVdVPF+fWZnnYUboATEn2xBVTOxmnowvYZE+jEzr0y16URw8upF1Wtw/t2if7065P3WB27dLliHvVbkbdqkucHtpt5zoH26+99sGmdQaq+kbvnIg8KiIHVPWoiBwAjjnXOFL/PiYitwGXA58GivIHQRAEZQw1THQ7cG29fS3w0TSBiOwWkb1r28CbgHtK8wdBEATlDBVN9F7gwyLyTuDPgZ8AEJEXATeq6lXAhcBtUk1sWQQ+qKq/n8s/gcBCZlnbIUknS203+tTNnazX9XrbWLvtWt/W6FO7vv+ufWvXp33buc71xSCdgao+DrxhyvEjwFX19kPA928kfxAEQdCNuV6OwrKQTJ0f5ZZIqJEkTetJQ8pG2GTBPFHYKewTH8tozrXyZC8+3YbUbg+rQaqPnRJvz5XoltowsWxBgXYTGjjapU9sRdqlq3Kae51Vu3R5hFm1a5+Yrc6Br12XOpf+XUu0SzXwtOujvbbs22bttc861xexHEUQBEEQnUEQBEEw58NEAqy9k8q5pyMzpT3nfLmrb1oXNHVHR47LPlotS5e7diHWanuvuSGMkejUc55uaTnlxjn3l76w87TLpSvUzlvx1dMNfO2sbum5LnUuS4l2E/o42nm6TdsvMc0W6dQ58LXro736xg3fXnOrDHdpr30QnkEQBEEQnUEQBEFwBgwTLdXTxtNvqlo3y3pcndyvVoRFzu2030ddTtJNd/O10O3MxVS379UZ/pm49GjqOU+39FwxnnYTwxuOdumyAB208/B0S8+1tWuXU6JdZ5e/RLtEH1c7T7eknNbhGesc+Nr10V5d+7ZBe83Rrb3OTngGQRAEwXx7BtUM5Goz90TiTXzMToj0ev00ht0+QZh45PSZxcYq2zwTTy5OWZp5iWmx99TSYJw+5p/6iSSnz6zaTSwE5miXxngXaZeZZ1BaF1ztRmUeRCftCuuCV+fA127WOgd+vfPqHPja9dFei+YZDNReS+pcei7bXnsgPIMgCIIgOoMgCIJgzoeJqnkGlTuVi29ueZMZ78t7IWVdw4mp5U488kQxbtyyXdah4zwD5/5Kp7d78c0Tq0x08Fxd7TLzB8Q5PrFfqJ07zyBTL/rUruv74yLt0uU67E5BnUvLKaWkzoGvXR/t1WM7tNfsPIMZ22tXwjMIgiAI5t0zEDe0tNXjmn4/1zsWzUBOX3zap5DFpeZaY//Fp3u9rqFqre3pYWtLyZel7Asqq52nW1pOMYX36mk38aK5R+083cDXLn2xV6Jd5yeygnu1ukFGu8I6XEpJnQNfuz7aa0lo6by01z4IzyAIgiCIziAIgiAYaJhIRM4D/iPwEuBh4H9U1W8nab6nTrPGS4FfUtV/IyL/BPifgG/W5/6hqt4xWVBmnkHmRajJnrmJ6f3o5IzGRmIxH8TOvZBSk6dL3HI2xN/GLbdedqX2nHqhuuzL9owNRdqN2lXT1S5dr79Eu9z3DKbnmLhXV7vcPINZtcu+kJyunSQfYfe0m7XOTVzbHnfqXFWWtadsobrS9loyz2Bu2msPDOUZXA/cqaoHgTvr/Raq+oCqvlxVXw78APAscJtJ8q/Xzk/tCIIgCIJihnqBfDXw2nr7FuBTwLsz6d8A/Jmqfn0jhdjQ0snQwOnbua8O+S+kMk8g7jLD6TWcdK1t37Z8qJoNb5w+83FCH6Y/iXm6peUU42mX03HkHM9do4Ntnm7V/vRLT75onp5n5jqXXryk/lQGbjyPY99kQMX0r3d5dS69tFfn0nyl2rlsg/aaN2/j7bUPhvIMLlTVowD17/2nSH8N8KHk2HUicreI3Cwi526GkUEQBGcKm+YZiMgngRdOOfWeDV5nGfgx4BfN4Q8A/4zqUeSfAf8S+Klp+Rccz6D1cGCO59YJ6fRxGzvOlxnLVe+JopdVEM0lpps2OZbrpPN0S8sppvCpytNucoXNjWvneVWebmkxrbHcTLoudS5LgXaaefdSVOem7RdQUufA166P9loUWjpQe8158l3aax9sWmegqm/0zonIoyJyQFWPisgB4FjmUm8Gvqiqj5prr2+LyL8HfrcPm4MgCM5Uhhomuh24tt6+FvhoJu3bSIaI6g5kjbcC9/RqXRAEwRnGUC+Q3wt8WETeCfw58BMAIvIi4EZVvare3wVcAfzPSf73icjLqfyrh6ecByoXa82bSt3J1ixGx+XKDxmZMLFWoekLO7Nv3NYJB7bDLMaWDcVL4pr7bl2rbZF1ilsv7wp0O5UNRdqlM0M97XJ6l4YT2uyO3RPfiG5dr7GoPZgwu3Z2OCG1u0i7ZKjE1a5DnUsp0S7N7WnXR3v1tNsO7bVVZA/ttQ8G6QxU9XGqCKH0+BHgKrP/LHD+lHRv31QDgyAIzjDmem0iaHrd0hU2s5OBSlYtzZ2T1rOPW7D3BNHHqqXe8YmXwV66nD4d3ml52k08BXvaFa6wmdPO+7uW3mvrhWYuXYc6l6NEu7Zu4GmXX2Fz4/Wu9F497fporx7bob3mQoa7tNc+GOqdQRAEQbCNmG/PQMw7g3SFzQ4TOOwYpJdl8onWGVscJ09szrhj6VNZLlStbY8p0o5NJ/Pbx3ayS2u8dvq1+qD9VJYZy7XaZVad7FO73CQoq904nZw2o3bZSWcGV7tUH0+7DrqV4tU58LXro72WaDcv7bUPwjMIgiAI5tszEGT9CaN0rLJT75iLJnCeGtJk7Uks3pT4jpPOnO3cZKCRefIoHR/vVbtEIE+7yUln/WmXqxeedqPkia1Eu5xlWW+0QLuJJ19Pu+wSFtMtzD15l9Q58LWL9jq5nWuvfTDXnQHMJlq67kmr8s/oSvfiinurIGbWjCm+9IyVLbtmzNDapf8gXe22XrdJG+yJ2etM39q1Tg2sXapbqyMdus7BprbXPohhoiAIgmD+PYOSiTDibBeTW6mwy9pCpWvGGEpXLXVfSBU+jXi6Tdsvou/1cXrUztMN+tWu+6qlBfc6q26Za5SuWpp9gbyJ2rmcQe11I4RnEARBEMy/Z7BG7sVVKSWhpZN5nJC/ZBXEzQzt82g9xCQPGq0VJJ08xeUUhke2ys+F/FntMi+aNxNPu4lVS508pfRa58DVbgjdwNeuj/Y6a707ndprH8x9Z7CmX9d1dDZeYFoxVjPncvkK8thkhRXf3uuq2uPJPIPWWkfTBSrVLR1OcLO17nU1c67g+KnO2WQF2qX36mk3Tq41q3bFeNpt4zpXnZuuXR/ttagjnZP22gcxTBQEQRDMt2cgZJ7MnDwzfywjdy4zvFF0vY7uqPsS3Wyvpuc2qFuunCyl9zqAdtnVJM221S77RNuhnOIXyN7xzPBG0fHMudwL5JI6B5urncs2aK+lH7dpHTfbaXvtg7nuDCxdFljLLYnrRTFMLjO8OvVc9stJBcdrI6baln6v18mSPd6aUlGYx9JaPiD9h1agnSTV3dOu0wJrmXh0T7vS+lN4q8XalWbytJuojwXalda5FM/uLtr10V6l4IJDtVdL9mGgg6ZdmfvOwBdzE9Q8lQH2ZVnHBtcnkvkv1qduxe8McgZsonZdXjR62uX/ic2mXXFup85V1yvrIDeLCQ02UbtObFF77bPO9cXcdwZr9PFypMsfsH2BDu576aVntC0tPbN47zB0cd+3CGtBZsHoTvRa56BX7Wa2DV+7Pv6qnTpSyya211nZjNLnvjMoEc2myVUat3Ll1iNJ/ztMy5M1rmwSjOae8u3lzHZu3HGjuqXltI6Xjnu3VonMFLxF2nm6ga9daSMtrXNZNku7zEqwlol3BgXazVrn0nQ57Yre8c1Je+2DQbo3EfkJEblXRMYiclkm3ZUi8oCIHBKR683x80TkEyLyYP373I3aMJLmZ1ORUfOzmXk60EWDQXQ7g7VTkfWfYk4T3bZ9vdvMPB3YbA2G8nXuAf4m8GkvgYgsAO8H3gy8DHibiLysPn09cKeqHgTurPeziEjrpwuiuv7T7QLS/Gzk3BbYltNnVt3sP7QN/VNrGzFdH3t8G2i3kXNbYVtWnx5161u7PtrrptW5U50rufQmtteuDPUN5PvhlC+FLgcOqepDddpbgauB++rfr63T3QJ8Cnh3eoHqb9VfNzrzGKSl5xdiObezC33q1sfYcvuCW/QysQN9v+jstc5Br9rlhom60Ld2vda7bd5e+2A7vzO4CHjE7B8GfqjevlBVjwKo6lER2T/tAnd/+UuPXXzenq9vrplBEASD812zXmDTOgMR+STwwimn3qOqHy25xJRjG+pCVfUFG0kfBEFwprJpnYGqvnHGSxwGLjH7FwNH6u1HReRA7RUcAI7NWFYQBMEZzfBB2j53AQdF5FIRWQauAW6vz90OXFtvXwuUeBpBEASBw1ChpW8VkcPAq4H/LCIfq4+/SETuAFDVFeA64GPA/cCHVfXe+hLvBa4QkQeBK+p9r6yp4amnEyJys4gcE5F7hrZlFkTkEhH5QxG5vw4t/oWhbeqCiOwUkc+JyFfq+/g/h7ZpFkRkQUS+JCK/O7QtXRGRh0XkT0TkyyLy+aHt6YqI7BORj4jIV+t28uotK1u3yZvszaAOT/1Tqg7jMJW38TZVvW9QwzaIiPwI8DTwm6r6fUPb05V6SO+Aqn5RRPYCXwB+/DT8ewiwW1WfFpEl4L8Av6CqnxnYtE6IyP8KXAacrapvGdqeLojIw8BlqvrY0LbMgojcAvyRqt5Yj4jsUtUntqLs7TxM1Afr4amqegJYC089rVDVTwPfGtqOWVHVo6r6xXr7KSqP76Jhrdo4WvF0vbtU/5yWT1UicjHw14Ebh7blTEdEzgZ+BLgJQFVPbFVHAPPfGUwLTz3t/vnMIyLyEuAVwGcHNqUT9dDKl6mCFz6hqqflfQD/Bvg/yC9icTqgwMdF5Asi8jNDG9ORlwLfBH69Hra7UUR2b1Xh894ZzByeGvSPiOwBfhv4+6r6naHt6YKqrqrqy6mi3C4XkdNu+E5E3gIcU9UvDG1LD7xGVV9JtWLBz9VDq6cbi8ArgQ+o6iuAZyhYXaEv5r0zyIWnBgNQj7H/NvBbqvo7Q9szK7Ub/yngymEt6cRrgB+rx9tvBV4vIv9hWJO6oapH6t/HgNuohohPNw4Dh42X+RGqzmFLmPfOIBeeGmwx9YvXm4D7VfVfDW1PV0TkBSKyr94+C3gj8NVBjeqAqv6iql6sqi+haht/oKp/d2CzNoyI7K4DEqiHVd5Etf7ZaYWq/gXwiIh8T33oDVTL72wJ23k5iplR1RURWQtPXQBuNuGppw0i8iGqtZguqENy/7Gq3jSsVZ14DfB24E/q8XaAf6iqdwxnUicOALfU0WojqrDn0zYscw64ELitXttoEfigqv7+sCZ15ueB36ofXh8CfnKrCp7r0NIgCIKgjHkfJgqCIAgKiM4gCIIgiM4gCIIgiM4gCIIgIDqDIAiCgOgMgiAIAqIzCIIgCIjOIAh6QUR+UETurr91sLv+zsFpt15RcOYSk86CoCdE5J8DO4GzqNaY+b8HNikIionOIAh6ol5C4C7geeC/U9XVgU0KgmJimCgI+uM8YA+wl8pDCILThvAMgqAnROR2qqWgL6X6vOd1A5sUBMXM9aqlQbBViMg7gBVV/WC9mul/FZHXq+ofDG1bEJQQnkEQBEEQ7wyCIAiC6AyCIAgCojMIgiAIiM4gCIIgIDqDIAiCgOgMgiAIAqIzCIIgCIjOIAiCIAD+f03BthnFUCY0AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Some examples using the constructors from the operators module\n",
    "fxxyy_op = de.operators.differentiate(f, x=2, y=2)\n",
    "total_int_f_op = de.operators.integrate(f, 'x', 'y')\n",
    "f00_op = de.operators.interpolate(f, x=0, y=0)\n",
    "\n",
    "fxxyy = fxxyy_op.evaluate()\n",
    "total_int_f = total_int_f_op.evaluate()\n",
    "f00 = f00_op.evaluate()\n",
    "\n",
    "print('Total integral:', total_int_f['g'][0,0])\n",
    "print('f at (x,y)=(0,0):', f00['g'][0,0])\n",
    "\n",
    "fxxyy.require_grid_space()\n",
    "plot_bot_2d(fxxyy);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Third, the `differentiate`, `integrate`, and `interpolate` field methods provide short-cuts for building and evaluating these operations, directly returning the resulting fields."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total integral: 12.566370614359172\n",
      "f at (x,y)=(0,0): 1.9999999999999727\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The same results, directly from field methods\n",
    "fxxyy = f.differentiate(x=2, y=2)\n",
    "total_int_f = f.integrate('x', 'y')\n",
    "f00 = f.interpolate(x=0, y=0)\n",
    "\n",
    "print('Total integral:', total_int_f['g'][0,0])\n",
    "print('f at (x,y)=(0,0):', f00['g'][0,0])\n",
    "\n",
    "fxxyy.require_grid_space()\n",
    "plot_bot_2d(fxxyy);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:dedalus]",
   "language": "python",
   "name": "conda-env-dedalus-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
